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M-6-6-2_November and March Calendar Activity and KEY
NOVEMBER AND MARCH CALENDAR ACTIVITY
Calendars have many patterns. Use the example November calendar to answer the following questions.
1. What are some number patterns you see on this calendar?
Su M
2. Look at the number 17. Substitute 17 for the variable x.
(x = 17)
3. How can you represent the number 18 as it relates to the
variable x?
4. How can you write the number 16 as it relates to the
variable x?
6
13
20
27
7
14
21
28
November
T W Th
1 2 3
8 9 10
15 16 17
22 23 24
29 30
F
4
11
18
25
5. How can you write an expression to represent the sum of these three consecutive numbers using x?
6. Write an equation for the sum of these three numbers using variables.
7. How can you write this equation in a different way?
(These are equivalent equations representing the same answer.)
8. With a partner, pick any three calendar numbers in a row.
9. Circle the numbers you chose on the calendar.
10. Find the sum of your three numbers.
11. Let the lowest of the three numbers be the variable x. Write it here:
x = _________
12. How can you represent the next two consecutive numbers as expressions including the variable x?
13. Write an equation for the sum of these three numbers using variables.
14. How can you write the equation in a different way?
(These are equivalent equations representing the same answer.)
Sa
5
12
19
26
M-6-6-2_November and March Calendar Activity and KEY
GUESS MY NUMBER! IT’S MAGIC!
Usually when you see a magic trick, you don’t know the secret behind it. Today you will learn the
“magic” behind a trick so you can impress your friends and family.
Four squares on the calendar have been chosen: 2, 3, 9,
and 10. When we find the sum of these four numbers, we
get 24. The four example numbers were written in a 2 × 2
grid below. In order to do this trick, we will let the
smallest number equal the variable m. Now we move to
the next number, which is 3.
How is 3 related to 2? (It is one greater.)
So if 2 is really m, then 3 is really one greater than m, or
m + 1. We will find the relationship of all the numbers to
2, and then we will write that relationship using m instead
of 2.
How is 9 related to 2? (It is 7 more than 2.)
So it is 7 more than m. Now we can say that 9 is m + 7.
What about the number 10?
Did you come up with m + 8?
Look at the grid below.
Do you agree with all of the expressions?
Su M
4
11
18
25
5
12
19
26
March
T W Th
1
6 7 8
13 14 15
20 21 22
27 28 29
15. Why is 3 equivalent to m + 1?
F
2
9
16
23
30
Sa
3
10
17
24
31
2
(m)
3
(m+1)
9
(m+7)
10
(m+8)
16. Why is 9 equivalent to m + 7?
17. Why is 10 equivalent to m + 8?
18. Write an equation for the sum of these four numbers using the expressions with variables instead of the
actual numbers. For instance, use m instead of 2.
19. Write as many other equations as you can that represent the sum of these four numbers.
(These are equivalent equations representing the same answer.)
20. Do all the combining and simplifying you can do for one of your equations. Did you get 4m + 16?
21. Now you try it. Pick any 4 numbers that form a 2 × 2 grid on a calendar and follow the same instructions.
You can predict the answer every time!
M-6-6-2_November and March Calendar Activity and KEY
HERE IS THE SECRET!
Think back to when you found the sum of the numbers 2, 3, 9, and 10. The sum was 24. The equation from
summing the four numbers with the variable m was 4m+16. The secret is:
4m + 16 = the sum of the four numbers
If you write the equation 4m + 16 = 24, you can solve for m. Use guess and check or inverse operations. The
solution is m = 2. If you have the expressions and you know m is 2, then you can find the four numbers that
were originally chosen. (You know that: m = 2, so substitute 2 into all the expressions for m and you get m + 1
= 3, m + 7 = 9, and m + 8 = 10.)
These are the four numbers originally picked: 2, 3, 9, and 10
Let’s try it. Go back to the calendar and choose 4 numbers that form a 2 × 2 grid. Write them down. (6, 7, 13,
and 14) What is their sum? (40) Let the lowest number = p. Write expressions with the variable p to represent
the other 3 numbers. Add up the four expressions and simplify as much as you can. (You should get 4p + 16.)
Set 4p + 16 = 40 and solve for p. After finding that p = 6, you can substitute back into the expressions and find
the original numbers:
6, 7, 13, and 14
If I tell you the sum of four numbers that form a 2 × 2 grid on the calendar is 96, what are the four numbers I
used? Use the same steps to figure out which four numbers I picked. Or, find another way to solve for the
mysterious four numbers. There are lots of patterns in a calendar, so there are many ways to solve this puzzle.
Which four numbers did I pick? _____ _____ _____ _____
Now that is magic!
M-6-6-2_November and March Calendar Activity and KEY
NOVEMBER AND MARCH CALENDAR ACTIVITY (KEY)
Calendars have many patterns. Use the example November calendar to answer the following questions.
1. What are some number patterns you see on this calendar?
The numbers are consecutive. The numbers alternate
even/odd in a column. The numbers in any column differ
by 7. The numbers on diagonal to the left differ by 6. The
numbers on diagonal to the right differ by 8.
2. Look at the number 17. Substitute 17 for the variable x.
(x = 17)
3. How can you represent the number 18 as it relates to the
variable x?
x+1
4. How can you write the number 16 as it relates to the
variable x?
x–1
Su M
6
13
20
27
7
14
21
28
November
T W Th
1 2 3
8 9 10
15 16 17
22 23 24
29 30
F
4
11
18
25
Sa
5
12
19
26
5. How can you write an expression to represent the sum of these three consecutive numbers using x?
x+x+1+x–1
6. Write an equation for the sum of these three numbers using variables.
x + x + 1 + x – 1 = 54
7. How can you write this equation in a different way?
(These are equivalent equations representing the same answer.)
3x = 54; 2x + x = 54
Answers for 8-14 will vary depending on numbers chosen. For demonstration purposes the, example below uses
numbers 20, 21, 22.
8. With a partner, pick any three calendar numbers in a row.
20, 21, 22
9. Circle the numbers you chose on the calendar.
10. Find the sum of your three numbers.
63
11. Let the lowest of the three numbers be the variable x. Write it here:
x = 20
12. How can you represent the next two consecutive numbers as expressions including the variable x?
x + 1, x + 2
13. Write an equation for the sum of these three numbers using variables.
x + x + 1 + x + 2 = 63
14. How can you write the equation in a different way?
(These are equivalent equations representing the same answer.)
3x + 3 = 63
M-6-6-2_November and March Calendar Activity and KEY
GUESS MY NUMBER! IT’S MAGIC! (KEY)
Usually when you see a magic trick, you don’t know the secret behind it. Today you will learn the
“magic” behind a trick so you can impress your friends and family.
Four squares on the calendar have been chosen: 2, 3, 9,
and 10. When we find the sum of these four numbers, we
get 24. The four example numbers were written in a 2 × 2
grid below. In order to do this trick, we will let the
smallest number equal the variable m. Now we move to
the next number, which is 3.
How is 3 related to 2? (It is one greater.)
So if 2 is really m, then 3 is really one greater than m, or
m + 1. We will find the relationship of all the numbers to
2, and then we will write that relationship using m instead
of 2.
How is 9 related to 2? (It is 7 more than 2.)
So it is 7 more than m. Now we can say that 9 is m + 7.
What about the number 10?
Did you come up with m + 8?
Look at the grid below.
Do you agree with all of the expressions?
Su M
4
11
18
25
5
12
19
26
March
T W Th
1
6 7 8
13 14 15
20 21 22
27 28 29
15. Why is 3 equivalent to m + 1?
F
2
9
16
23
30
Sa
3
10
17
24
31
2
(m)
3
(m+1)
9
(m+7)
10
(m+8)
because 2 is m, and 3 is one more than 2
16. Why is 9 equivalent to m + 7?
because 2 is m, and 9 is a week later (+7)
17. Why is 10 equivalent to m + 8?
because 2 is m, and 10 is 8 days later (+8)
18. Write an equation for the sum of these four numbers using the expressions with variables instead of the
actual numbers. For instance, use m instead of 2.
m+m+1+m+7+m+8 =24
19. Write as many other equations as you can that represent the sum of these four numbers.
(These are equivalent equations representing the same answer.)
Some answers include:
4m + 16 = 24, 2m + 1 + m + m + 15 = 24, 2m +2m + 16 = 24, 2m + 2m + 8 + 8 = 24,
3m + 8 + 8 + m = 24, 4m + 1+ 7 + 8 = 24
20. Do all the combining and simplifying you can do for one of your equations. Did you get 4m + 16?
Answers will vary.
21. Now you try it. Pick any 4 numbers that form a 2 × 2 grid on a calendar and follow the same instructions.
You can predict the answer every time!
M-6-6-2_November and March Calendar Activity and KEY
HERE IS THE SECRET! (KEY)
Think back to when you found the sum of the numbers 2, 3, 9, and 10. The sum was 24. The equation from
summing the four numbers with the variable m was 4m+16. The secret is:
4m + 16 = the sum of the four numbers
If you write the equation 4m + 16 = 24, you can solve for m. Use guess and check or inverse operations. The
solution is m = 2. If you have the expressions and you know m is 2, then you can find the four numbers that
were originally chosen. (You know that: m = 2, so substitute 2 into all the expressions for m and you get m + 1
= 3, m + 7 = 9, and m + 8 = 10.)
These are the four numbers originally picked: 2, 3, 9, and 10
Let’s try it. Go back to the calendar and choose 4 numbers that form a 2 × 2 grid. Write them down. (6, 7, 13,
and 14) What is their sum? (40) Let the lowest number = p. Write expressions with the variable p to represent
the other 3 numbers. Add up the four expressions and simplify as much as you can. (You should get 4p + 16.)
Set 4p + 16 = 40 and solve for p. After finding that p = 6, you can substitute back into the expressions and find
the original numbers:
6, 7, 13, and 14
If I tell you the sum of four numbers that form a 2 × 2 grid on the calendar is 96, what are the four numbers I
used? Use the same steps to figure out which four numbers I picked. Or, find another way to solve for the
mysterious four numbers. There are lots of patterns in a calendar, so there are many ways to solve this puzzle.
Which four numbers did I pick? _____ _____ _____ _____
Answers will vary.
.